{"paper":{"title":"Holonomy groups of flat manifolds with $R_\\infty$ property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrzej Szczepa\\'nski, Rafa{\\l} Lutowski","submitted_at":"2011-04-29T15:28:48Z","abstract_excerpt":"Let $M$ be a flat manifold. We say that $M$ has $R_\\infty$ property if the Reidemeister number $R(f) = \\infty$ for every homeomorphism $f \\colon M \\to M.$ In this paper, we investigate a relation between the holonomy representation $\\rho$ of a flat manifold $M$ and the $R_\\infty$ property. In case when the holonomy group of $M$ is solvable we show that, if $\\rho$ has a unique $\\mathbb{R}$-irreducible subrepresentation of odd degree, then $M$ has $R_\\infty$ property. The result is related to conjecture 4.8 from [1].\n  [1] K. Dekimpe, B. De Rock, P. Penninckx, \\emph{The $R_{\\infty}$ property for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5661","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}